Resonators are used in a variety of applications in mobile communications devices. In particular, resonators are often used in filters for mobile communications devices. Resonators for filters generally demand a high quality factor (Q) and selectivity. One conventional type of resonator is illustrated in FIG. 1. Specifically, FIG. 1 shows a cavity resonator 10. The cavity resonator 10 includes an input port 12, an output port 14, and a resonant cavity 16. Radio frequency (RF) signals provided at the input port 12 enter the resonant cavity 16. The RF signals bounce between the walls of the resonant cavity 16, forming standing waves at a resonant frequency that is determined by a diameter DC of the resonant cavity 16 and a height HC of the resonant cavity 16, among other factors that will be understood by those of ordinary skill in the art. The standing waves are then propagated to the output port 14. While the cavity resonator 10 provides a high quality factor, it is too large to fit into a mobile communications device. Further, the cavity resonator 10 is not tunable, as the resonant response thereof is fixed by the geometry of the device.
An additional type of conventional resonator is illustrated in FIG. 2 and FIG. 3. Specifically, FIG. 2 and FIG. 3 show an LC resonator 18. The LC resonator 18 includes an inductive element 20 and a capacitive element 22. A first parasitic resistance 24A and a second parasitic resistance 24B are also illustrated. A signal provided to the LC resonator 18 will oscillate between storage in the magnetic field of the inductive element 20 and the electric field of the capacitive element 22. The particular inductance and capacitance, respectively, of the inductive element 20 and the capacitive element 22 determine the speed at which this oscillation occurs, and thus the resonant frequency of the LC resonator 18. While the LC resonator 18 is significantly more compact than the cavity resonator 10 and may be tuned by altering the capacitance of the capacitive element 22, the quality factor of the LC resonator 18 is generally quite low due to the parasitic resistance 24 between the inductive element 20 and the capacitive element 22 and the internal resistive losses of the inductor element 20 and the capacitive element 22. In particular, FIG. 3 shows how the LC resonator 18 is normally fabricated, wherein the inductive element 20 is provided on a laminate 26, and connected to the capacitive element 22 on a separate chip 28 via a number of interconnects 30. The parasitic resistance 24 is generally due to the length and quality of the interconnects 30, as well as the internal resistance of the components themselves as discussed above. As energy is passed between the inductive element 20 and the capacitive element 22, the parasitic resistance 24 dissipates a part of this energy, thus damping the resonant response and lowering the quality factor of the LC resonator 18.
Specifically, Equation (1) illustrates the relationship between parasitic resistance and quality factor:
                    Q        =                                            1              R                        ⁢                                          L                C                                              =                                                    ω                0                            ⁢              L                        R                                              (        1        )            where Q is the quality factor of the LC resonator 18, R is the parasitic resistance of the first parasitic resistance 24A and the second parasitic resistance 24B, L is the inductance of the inductive element 20, C is the capacitance of the capacitive element 22, and ω0 is the resonant frequency of the LC resonator 18. As Equation (1) illustrates, the quality factor is inversely proportional to the parasitic resistance. Due to the length and quality of the interconnects 30 discussed above, the quality factor of the LC resonator 18 is limited.
Accordingly, there is a need for a resonator with a high quality factor and a small form factor.